Definition:Extended Real Number Line/Definition 1
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Definition
The extended real number line $\overline \R$ is defined as:
- $\overline \R := \R \cup \set {+\infty, -\infty}$
that is, the set of real numbers together with two auxiliary symbols:
- $+\infty$, positive infinity
- $-\infty$, negative infinity
such that:
- $\forall x \in \R: x < +\infty$
- $\forall x \in \R: -\infty < x$
Also see
- Results about extended real numbers can be found here.
Sources
- 2005: René L. Schilling: Measures, Integrals and Martingales ... (previous) ... (next): $\S 8$